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Christopher Nerz

Profile picture of Christopher Nerz

About me

Current Website

https://chris.nerz.me

Address

Lindstedtsvägen 25
Department of mathematics
KTH
100 44  Stockholm
Sweden

Research interests

  • Mathematical general relativity
  • Differential geometry
  • Geometric analysis

Current research

Currently, I'm working with 'nice' foliations of asymptotically Euclidean or asymptotically hyperbolic Riemannian (or Lorentzian) manifolds and study for example their evolution in time (under Einstein's equations). For example, I use the unique foliation by stable spheres of constant mean curvature introduced by Huisken-Yau in 1996.

Publications

  1. Nerz, Geometric characterizations of asymptotically hyperbolic Riemannian 3-manifolds by the existence of a suitable CMC-foliation [preprint (2017)]
  2. Nerz, Existence and uniqueness of constant mean curvature foliations of general asymptotically hyperbolic 3-manifolds [preprint (2016)]
  3. Nerz, Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry [preprint (2015) (accepted by JDG)]
  4. Nerz, Geometric characterizations of asymptotic flatness and linear momentum in general relativity [J. Funct. Ana. (2015), preprint (2014)]
  5. Nerz, Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry [Cal. of Var. and PDE's (2015), preprint (2014)]
  6. Cederbaum, Nerz, Explicit Riemannian manifolds with unexpectedly behaving center of mass [Ann. Henri Poincaré (2014), preprint (2013)]
  7. Nerz, Time evolution of ADM and CMC center of mass in general relativity [preprint (2013)]

My PhD thesis (german, 2014) Blätterungen asymptotisch flacher Mannigfaltigkeiten und ihre Evolution (Foliations of asymptotically flat manifolds and their evolution in time).

My Diploma thesis (german, 2011) Maß­zerlegung, Integralräume und dynamische Systeme (De­com­posi­tion of measures, integral-spaces and dynamical systems).

Miscellaneous

  • I wrote a (german) lecture note based on the lectures Differential geometry I-II lectured by Prof. Dr. Franz Pedit.

LaTeX

You are welcome to use the following LaTeX packages in your work as long as you give credit to the author of these packages (as defined by the Creative Commons attribution alone license, CC BY). Just copy the corresponding .sty-file in the directory of the current .tex-file (or install it correctly as LaTeX-Package). Here, 'Package (German)' only means that all comments in the LaTeX code are written in German.

  1. C. N., bracket-hack, 'automatically' inserts 'missing' \left and \right commands for any brace (,),lbrace,rbrace used in displaystyle math (align,align* etc.) [Package, Description (English), .sty-file]
  2. C. N., simpletensors, allows to define tensor-commands: commands able to use left sub- and superindices as optional arguments and correctly parse (multiple) right indices [Package, Description (English) (German), .sty-file]
  3. C. N., PMsimpletensors, can be used instead of simpletensors (identical syntax), but does not use the xparse package. Therefore, it is compatible with each LaTeX-system (since LaTeX 2.09) while simpletensors needs LaTeX 2\(_\varepsilon\). However, it is less efficient than simpletensors and can produce cryptic error messages if used wrongly [Package, Description (English), .sty-file]
  4. C. N., auto-equation label, allows to label equations such that they are only tagged if refered to [Package, Description (English), .sty-file]
  5. C. N., tensors extened, allows to define tensor-commands with (almost) arbitrary commands: commands able to use left sub- and superindices as optional arguments and correctly parse (multiple) right indices and complex arguments [Package (German)]
  6. C. N., multiline-underbrace, allows to use underbraces in align and align* environments, which contain multiple lines [Package (German)]
  7. C. N., partial, replaces the partial command such that \partial_i is the correct i-th derivation, allowing optional arguments to replace the coordinate, the order of the derivative etc. [Package (German)]
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